Algorithm EvolveCluster (Nordahl et al. 2022)

• \(D\) is a continuous stream of data, segmented into time-based chunks \(D_0, D_1, \ldots, D_t, t\rightarrow \infty\).

• \(D_0\) is partitioned in \(k\) clusters (via \(k\)-means): \(C_{0}=\{C_{00},\dots, C_{0k}\}\).

• For each segment \(D_t, t\neq0\), \(k\)-means is initialized using centroids from \(C_{t-1}\)

• Centroids of \(C_{t-1}\) are removed and empty clusters are deleted.

• New centroides are calculated and the partition \(C_t\) is refined:

  • Any cluster should be split into two? Apply \(2\)-means for each cluster with the two furthest points as initial centroids: \(C'_t\)

  • The two options of partitions are evaluated by a validation measure (e.g. Silhouette index SI): \(\text{If } \text{SI}(C'_t) > \text{SI}(C_t) + \tau \Rightarrow C_t \leftarrow C'_t\)

Goal: Detect race breaks

Input: Time gap from race leader

• Splits are evaluated within each cluster.
• Observations (swimmers) are sorted by gap to leader.
• A split occurs if two consecutive swimmers are separated by more than \(\tau\)

Refinement strategy:

Let \(x_i\) and \(x_{i+1}\) be consecutive swimmers in cluster \(C_l\). If \(d(x_i, x_{i+1}) > \tau\), split the cluster at that point.

\(\tau\) can also be selected following a validation measure (SI, Dunn index, etc.)

Advantages:

• \(\tau\) is interpretable as the minimum meaningful gap between swimmers

🖥️ Live demo 🤞🏻

• We explored both static and dynamic clustering approaches on competitive swimming data
  
• From splits, we identified strategic groupings of swimmers based on how they paced their races
  
• By analyzing gap-to-leader as streaming data, we captured race dynamics and key moments of separation
  
• The combination of both views offers a richer understanding of performance patterns

Despite the limited data, our analysis provides:

• Tactical insights into pacing strategies
• Recommendations for swimmers and coaches
• A framework for interpretable and adaptable analytics